Color gauge invariance in the Drell-Yan process
Daniel Boer, P. J. Mulders
TL;DR
The paper demonstrates that a color gauge invariant factorization of the Drell–Yan cross section, including twist-three and transverse-momentum dependent aspects, can be achieved by expressing the hadron tensor through color gauge invariant, nonlocal correlators with Wilson lines. Ward identities are shown to extend collinear gluon exponentiation to next-to-leading twist, validating a gauge-invariant framework to all orders in $oldsymbol{ ext{α}_s}$ and clarifying the treatment of soft gluon poles. It resolves a disagreement between prior treatments of a single-spin asymmetry by arguing that the derivative term arises from an unnecessary $n_-$-independence constraint. The results connect to established leading-twist factorization and Sudakov resummation, supporting a comprehensive, gauge-invariant approach to DY in the subleading regime and beyond.
Abstract
We consider the color gauge invariance of a factorized description of the Drell-Yan process cross section. In particular, we focus on the next-to-leading twist contributions for polarized scattering and on the cross section differential in the transverse momentum of the lepton pair in the region where the transverse momentum is small compared to the hard scale. The hadron tensor is expressed in terms of manifestly color gauge invariant, nonlocal operator matrix elements and a color gauge invariant treatment of soft gluon poles is given. Also, we clarify the discrepancy between two published results for a single spin asymmetry in the Drell-Yan cross section. This asymmetry arises if such a soft gluon pole is present in a specific twist-three hadronic matrix element.